SatoTate Equidistribution for Families of Automorphic Representations through the Stable Trace Formula
Abstract
In arXiv:1208.1945, Shin and Templier proved certain equidistribution bounds on local components of certain families of automorphic representations. We extend their weightaspect results to families of automorphic representations where the Archimedean component is restricted to a single discreteseries representation instead of an entire $L$packet. We do this by using a socalled "hyperendoscopy" version of the stable trace formula developed by Ferrari. The main technical difficulties are defining a version of hyperendoscopy that works for groups without simply connected derived subgroup and bounding the values of transfers of unramified functions. We also present an extension of Arthur's simple trace formula for test functions with EulerPoincaré component at infinity to noncuspidal groups since it does not seem to appear elsewhere in the literature.
 Publication:

arXiv eprints
 Pub Date:
 October 2019
 arXiv:
 arXiv:1910.10800
 Bibcode:
 2019arXiv191010800D
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Representation Theory;
 11F55;
 (primary) 11F70;
 11F72;
 11F75;
 22E50;
 22E55 (secondary)
 EPrint:
 74 pages. Beyond lots of typo corrections, there were some material corrections in sections 2.1, 6.4, and 10.1. 10.1 in particular had parts that were dependent on a reference that has been found to have a gap